Chapter 2
I demonstrate by means of philosophy that the earth is round, and is inhabited on all sides; that it is insignificantly small, and is borne through the stars.
Johannes Kepler

In this chapter we begin to trace the historical developments of modern cosmological theory. The first attempt to construct a systematic cosmology that was grounded in physical theory was the model of Aristotle. Aristotle developed a theory of motion, and defined the concepts of "natural motion" and "force." In Aristotle's view, the Earth was the center of the universe and the center of all natural motions. Motions on the Earth were linear and finite, while the heavenly bodies executed perfect circles forever. Aristotle's Periodic TableThe stars and planets were composed of a perfect element called "ether," whereas Earthly objects were made up of varying combinations of the four ancient elements of earth, air, fire and water; a body's motion was a consequence of its composition. Although our modern definitions of these concepts are quite different from Aristotle's, natural motion and force remain fundamental to our understanding of the structure and evolution of the universe. Aristotle's Earth-centered world view was embodied in the detailed model of Ptolemy, with its deferents, epicycles, and eccentrics, all designed to predict the complicated celestial motions of the planets while still requiring motion in the heavens to be built upon circles.

The Aristotelian cosmological system was consistent with his physics. Although Aristotle's cosmology is quite different from the modern point of view, in what ways is it consistent with modern ideas? How did it differ?

During the Renaissance, humanity's cosmological model changed dramatically. The first blow in the "Scientific Revolution" was struck by Copernicus, whose Sun-centered model of the heavens gained rapid ascendancy in Renaissance Europe. What were some of the motivations for Copernicus to propose such a grand change to the prevailing concepts of the universe?

Tycho Brahe's observations of a supernova that appeared in 1572 helped to end the belief in the Aristotelean unchanging perfection of the celestial realm. How would you feel if you observed something that so challenged a basic tenet of your world view? In Tycho's own words:

Amazed, and as if astonished and stupefied, I stood still, gazing for a certain length of time with my eyes fixed intently upon it and noticing that same star placed close to the stars which antiquity attributed to Cassiopeia. When I had satisfied myself that no star of that kind had ever shone forth before, I was led into such perplexity by the unbelievability of the thing that I began to doubt the faith of my own eyes.

Tycho Brahe's detailed naked eye observations of the heavens provided the data that Kepler used to derive his laws of planetary motion. Kepler's laws of planetary made it possible for the first time for humans to understand the paths of the "wanderers" across the sky.

  • Kepler's First Law Planets orbit the Sun along elliptical paths, with the Sun at one focus of the ellipse.
  • Kepler's Second Law (Law of Equal Areas) The area swept out by the line joining a planet and the Sun is equal for equal intervals of time.
  • Kepler's Third Law (Harmonic Law) The square of the orbital period in years equals the cube of the length of the semi major (half the longer) axis of the orbit.
A consequence of Kepler's second law is that planets orbit more slowly the more distant they are from the Sun. The third law enables the period of a planet, comet, or asteroid to be computed once observations establish the length of the semi major axis of its orbit. These laws were among the greatest quantitative achievements of the Renaissance.

Kepler also observed a supernova, only 32 years after Tycho, in 1604. The next supernova visible to the naked eye did not occur until 1987 when a star exploded in the nearby irregular galaxy known as the Large Magellanic Cloud.

Kepler and Galileo were contemporaries, though Kepler was more of a theorist and Galileo was primarily an observer. Galileo was the first to make serious scientific use of the telescope, an instrument which provided observations that challenged the Ptolemaic model of the heavens. (Kepler was unable to afford to purchase a telescope, a prohibitively expensive device at the time, though he was able to borrow one for a summer from a visiting nobleman. Galileo promised for several years to make a telescope for Kepler, but never got around to fulfilling his promise.) Galileo observed craters on the Moon, demonstrating that it was not a perfect, smooth sphere; he also gave the large lunar plains the name of "maria" (seas) because he thought they might be filled with water. He also found that the Milky Way was not a solid band of light but was filled with myriad stars, too small to be resolved by the unaided eye. Another key observation by Galileo was that Venus went through a full cycle of phases, just like the Moon; this was impossible in the Ptolemaic model but was required by the Copernican model, since Venus is between the Earth and the Sun in the latter. But one of Galileo's most important discoveries was of the four largest satellites of Jupiter, now called the Galilean moons. These bodies demonstrated that the Earth was not the only center of motion in the universe, thus refuting one of the important tenets of Ptolemaic-Aristotelian cosmology and physics.

These new observations challenged the Aristotelean notions of motion. Reconciling the new cosmology with the physics of motion required Galileo to study mechanics. From direct observation and careful reasoning, he was able to arrive at the conclusion that all bodies fall at the same rate, if air resistance is negligible. This principle, now called the equivalence principle, is one of the foundations of the general theory of relativity. Galileo also realized that motion might not be easily detectable by observers partaking of that motion, i.e., that motion is relative. This meant it was possible for us to be on a moving Earth, yet unaware of its motion. Galileo never succeeded in working out the full laws of motion. But a few months after Galileo's death, Isaac Newton was born on a farm in Lincolnshire, England, beginning a life that would complete the Copernican Revolution with the fundamental laws of physics and gravitation that govern the universe under most conditions.

For more information see Questions and Answers related to Chapter 2.

To learn more about the life of Galileo go to the Galileo Project Home page. Bibliographic information about Copernicus , Johannes Kepler , and Tycho Brahe are also available.

Original content © 2005 John F. Hawley